Analytic solutions for the valence subband mixing at the zone center of a GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum well under uniaxial stress perpendicular to the growth direction

Using the envelope-function approach, we present a theoretical analysis of the effects of uniaxial stress applied along the [100] direction on the zone-center valence states of a type-I GaAs/${\mathrm{Ga}}_{\mathit{x}}$${\mathrm{Al}}_{1\mathrm{-}\mathit{x}}$As [001] quantum well. The resulting strain reduces the symmetry and causes mixing between heavy and light holes which can be described approximately within the ${\mathrm{\Gamma }}_8$ subspace by a 4×4 Luttinger-Kohn Hamiltonian in conjunction with the correct 4×4 Bir-Pikus strain Hamiltonian. An approximate analytic solution is found by expanding the finite-stress solutions in terms of the zero-stress eigenstates. This representation allows a detailed analysis of the strain-induced coupling terms between heavy and light holes. By neglecting all small coupling terms it is possible to describe the hole mixing at any stress in terms of independent two-level systems. In this case the Hamiltonian becomes block diagonal and can easily be diagonalized analytically. Within the experimentally accessible pressure range of 10 kbar, these simple analytic solutions deviate from the large-scale numerical solutions by less than 1%. The coupling of the spin-orbit split-off states in the ${\mathrm{\Gamma }}_7$ subspace to the ${\mathrm{\Gamma }}_8$ subspace at finite and zero stress is then taken into account via second-order perturbation theory. Comparison of the theoretical results with experimental photoluminescence data shows good agreement and provides strong evidence for the stress-induced hole mixing. © 1996 The American Physical Society.